Courant bracket

The Courant bracket is a mathematical operation that arises in the context of differential geometry and the theory of Dirac structures. It is named after the mathematician Richard Courant and plays a significant role in the study of symplectic geometry and Poisson geometry, as well as in the theory of integrable systems. In a more formal context, the Courant bracket is defined on sections of a specific vector bundle called the Courant algebroid.